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Chapter 4: Q. 8 (page 398)
State the Second Fundamental Theorem of Calculus and its importance.
The Second Fundamental Theorem states that if f is continuous on [a,b] then for all x=[a,b], then F is continuous on [a,b] and differentiable on (a,b) and F is an antiderivative of f l.e. F(x) = f(x).
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Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Prove Theorem 4.13(b): For any real numbers a and b, we have. Use the proof of Theorem 4.13(a) as a guide.
Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating
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Prove Theorem 4.13(c): For any real numbers a and b, Use the proof of Theorem 4.13(a) as a guide.
Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: ).
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